Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13×C19 · Schur multiplier (H2) = C1 |
| direct product | C13×C19×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C13×C19) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C13×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C19 | AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7 | C2×C3×C13×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C19 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C13×C19 | |
32 conjugacy classes of subgroups.
1729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 73);